Properties

Label 1176i
Number of curves $6$
Conductor $1176$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1176i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1176.i5 1176i1 \([0, 1, 0, 33, -78]\) \(2048/3\) \(-5647152\) \([2]\) \(192\) \(-0.018971\) \(\Gamma_0(N)\)-optimal
1176.i4 1176i2 \([0, 1, 0, -212, -960]\) \(35152/9\) \(271063296\) \([2, 2]\) \(384\) \(0.32760\)  
1176.i2 1176i3 \([0, 1, 0, -3152, -69168]\) \(28756228/3\) \(361417728\) \([2]\) \(768\) \(0.67418\)  
1176.i3 1176i4 \([0, 1, 0, -1192, 14720]\) \(1556068/81\) \(9758278656\) \([2, 2]\) \(768\) \(0.67418\)  
1176.i1 1176i5 \([0, 1, 0, -18832, 988448]\) \(3065617154/9\) \(2168506368\) \([2]\) \(1536\) \(1.0208\)  
1176.i6 1176i6 \([0, 1, 0, 768, 60192]\) \(207646/6561\) \(-1580841142272\) \([2]\) \(1536\) \(1.0208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1176i have rank \(0\).

Complex multiplication

The elliptic curves in class 1176i do not have complex multiplication.

Modular form 1176.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.